Question

By what number should (–15)^–1 be divided so that the quotient may be equal to (–5)^–1?

Answer 1

Let x be the number divide (–15)^–1 to get (–5)^–1 as a quotient.

So, (–15)^–1 ÷ x = (–5)^–1  

⇒ `1/(-15) xx 1/x = 1/-5`  ...`[∵ a^-m = 1/a^m]`

⇒ `1/x = 1/-5 ÷ 1/(-15)`

⇒ `1/x = 1/-5 xx (-15)/1`

⇒ `1/x = 3`

⇒ `x = 1/3`